#4249: Inconsistency in number field integral bases
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Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2
Component: number theory | Keywords: number fields
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This is unacceptable (in my opinion):
{{{
sage: K.<a>=NumberField(x^2+23)
sage: K.integral_basis()
[1, 1/2*a + 1/2]
sage: K.ring_of_integers().basis()
[1/2*a + 1/2, a]
}}}
I think these should be the same. The problem is that K.integral_basis()
gets the basis from pari, but when the ring_of_integers is constructed it
uses that basis in the constructions but then creates its own, different,
basis!
Suggested solution: make the existing integral_basis() function an
internal one used by the ring_of_integers() function only, and have
K.integra_basis() return the basis of the ring of integers instead.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4249>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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